TSTP Solution File: SET666+3 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET666+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 14:35:07 EDT 2023
% Result : Theorem 0.21s 0.58s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 37
% Syntax : Number of formulae : 78 ( 8 unt; 27 typ; 0 def)
% Number of atoms : 206 ( 0 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 259 ( 104 ~; 104 |; 16 &)
% ( 8 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 23 >; 11 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 4 con; 0-2 aty)
% Number of variables : 96 ( 2 sgn; 46 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
set_type: $i ).
tff(decl_23,type,
ilf_type: ( $i * $i ) > $o ).
tff(decl_24,type,
cross_product: ( $i * $i ) > $i ).
tff(decl_25,type,
subset_type: $i > $i ).
tff(decl_26,type,
relation_type: ( $i * $i ) > $i ).
tff(decl_27,type,
identity_relation_of: $i > $i ).
tff(decl_28,type,
subset: ( $i * $i ) > $o ).
tff(decl_29,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_30,type,
member: ( $i * $i ) > $o ).
tff(decl_31,type,
binary_relation_type: $i ).
tff(decl_32,type,
identity_relation_of_type: $i > $i ).
tff(decl_33,type,
relation_like: $i > $o ).
tff(decl_34,type,
power_set: $i > $i ).
tff(decl_35,type,
member_type: $i > $i ).
tff(decl_36,type,
empty: $i > $o ).
tff(decl_37,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_38,type,
esk2_1: $i > $i ).
tff(decl_39,type,
esk3_0: $i ).
tff(decl_40,type,
esk4_1: $i > $i ).
tff(decl_41,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_42,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_43,type,
esk7_1: $i > $i ).
tff(decl_44,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_45,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_46,type,
esk10_1: $i > $i ).
tff(decl_47,type,
esk11_1: $i > $i ).
tff(decl_48,type,
esk12_0: $i ).
fof(p22,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22) ).
fof(p18,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p18) ).
fof(p24,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p24) ).
fof(p12,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ilf_type(X2,subset_type(X1))
<=> ilf_type(X2,member_type(power_set(X1))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ! [X3] :
( ilf_type(X3,subset_type(cross_product(X1,X2)))
=> ilf_type(X3,relation_type(X1,X2)) )
& ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ilf_type(X4,subset_type(cross_product(X1,X2))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(p6,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ilf_type(X2,identity_relation_of_type(X1))
<=> ilf_type(X2,relation_type(X1,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6) ).
fof(p14,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( subset(X1,X2)
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X1)
=> member(X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p14) ).
fof(p3,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> subset(identity_relation_of(X1),cross_product(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
fof(prove_relset_1_29,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ilf_type(identity_relation_of(X1),identity_relation_of_type(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_29) ).
fof(p16,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X1,power_set(X2))
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X1)
=> member(X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p16) ).
fof(c_0_10,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[p22]) ).
fof(c_0_11,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[p18]) ).
fof(c_0_12,plain,
! [X55,X56] :
( ( ~ empty(X55)
| ~ ilf_type(X56,set_type)
| ~ member(X56,X55)
| ~ ilf_type(X55,set_type) )
& ( ilf_type(esk11_1(X55),set_type)
| empty(X55)
| ~ ilf_type(X55,set_type) )
& ( member(esk11_1(X55),X55)
| empty(X55)
| ~ ilf_type(X55,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])])]) ).
fof(c_0_13,plain,
! [X59] : ilf_type(X59,set_type),
inference(variable_rename,[status(thm)],[p24]) ).
fof(c_0_14,plain,
! [X27,X28] :
( ( ~ ilf_type(X28,subset_type(X27))
| ilf_type(X28,member_type(power_set(X27)))
| ~ ilf_type(X28,set_type)
| ~ ilf_type(X27,set_type) )
& ( ~ ilf_type(X28,member_type(power_set(X27)))
| ilf_type(X28,subset_type(X27))
| ~ ilf_type(X28,set_type)
| ~ ilf_type(X27,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p12])])])]) ).
fof(c_0_15,plain,
! [X41,X42] :
( ( ~ ilf_type(X41,member_type(X42))
| member(X41,X42)
| empty(X42)
| ~ ilf_type(X42,set_type)
| ~ ilf_type(X41,set_type) )
& ( ~ member(X41,X42)
| ilf_type(X41,member_type(X42))
| empty(X42)
| ~ ilf_type(X42,set_type)
| ~ ilf_type(X41,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
cnf(c_0_16,plain,
( ~ empty(X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X1)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_18,plain,
! [X5,X6,X7,X8] :
( ( ~ ilf_type(X7,subset_type(cross_product(X5,X6)))
| ilf_type(X7,relation_type(X5,X6))
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) )
& ( ~ ilf_type(X8,relation_type(X5,X6))
| ilf_type(X8,subset_type(cross_product(X5,X6)))
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])])]) ).
cnf(c_0_19,plain,
( ilf_type(X1,subset_type(X2))
| ~ ilf_type(X1,member_type(power_set(X2)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( ilf_type(X1,member_type(X2))
| empty(X2)
| ~ member(X1,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17]),c_0_17])]) ).
fof(c_0_22,plain,
! [X17,X18] :
( ( ~ ilf_type(X18,identity_relation_of_type(X17))
| ilf_type(X18,relation_type(X17,X17))
| ~ ilf_type(X18,set_type)
| ~ ilf_type(X17,set_type) )
& ( ~ ilf_type(X18,relation_type(X17,X17))
| ilf_type(X18,identity_relation_of_type(X17))
| ~ ilf_type(X18,set_type)
| ~ ilf_type(X17,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p6])])])]) ).
cnf(c_0_23,plain,
( ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X1,subset_type(cross_product(X2,X3)))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
( ilf_type(X1,subset_type(X2))
| ~ ilf_type(X1,member_type(power_set(X2))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_17]),c_0_17])]) ).
cnf(c_0_25,plain,
( ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_17]),c_0_17])]),c_0_21]) ).
fof(c_0_26,plain,
! [X31,X32,X33] :
( ( ~ subset(X31,X32)
| ~ ilf_type(X33,set_type)
| ~ member(X33,X31)
| member(X33,X32)
| ~ ilf_type(X32,set_type)
| ~ ilf_type(X31,set_type) )
& ( ilf_type(esk5_2(X31,X32),set_type)
| subset(X31,X32)
| ~ ilf_type(X32,set_type)
| ~ ilf_type(X31,set_type) )
& ( member(esk5_2(X31,X32),X31)
| subset(X31,X32)
| ~ ilf_type(X32,set_type)
| ~ ilf_type(X31,set_type) )
& ( ~ member(esk5_2(X31,X32),X32)
| subset(X31,X32)
| ~ ilf_type(X32,set_type)
| ~ ilf_type(X31,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p14])])])])]) ).
fof(c_0_27,plain,
! [X12] :
( ~ ilf_type(X12,set_type)
| subset(identity_relation_of(X12),cross_product(X12,X12)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p3])]) ).
fof(c_0_28,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ilf_type(identity_relation_of(X1),identity_relation_of_type(X1)) ),
inference(assume_negation,[status(cth)],[prove_relset_1_29]) ).
cnf(c_0_29,plain,
( ilf_type(X1,identity_relation_of_type(X2))
| ~ ilf_type(X1,relation_type(X2,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
( ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X1,subset_type(cross_product(X2,X3))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_17]),c_0_17])]) ).
cnf(c_0_31,plain,
( ilf_type(X1,subset_type(X2))
| ~ member(X1,power_set(X2)) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_32,plain,
! [X36,X37,X38] :
( ( ~ member(X36,power_set(X37))
| ~ ilf_type(X38,set_type)
| ~ member(X38,X36)
| member(X38,X37)
| ~ ilf_type(X37,set_type)
| ~ ilf_type(X36,set_type) )
& ( ilf_type(esk6_2(X36,X37),set_type)
| member(X36,power_set(X37))
| ~ ilf_type(X37,set_type)
| ~ ilf_type(X36,set_type) )
& ( member(esk6_2(X36,X37),X36)
| member(X36,power_set(X37))
| ~ ilf_type(X37,set_type)
| ~ ilf_type(X36,set_type) )
& ( ~ member(esk6_2(X36,X37),X37)
| member(X36,power_set(X37))
| ~ ilf_type(X37,set_type)
| ~ ilf_type(X36,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p16])])])])]) ).
cnf(c_0_33,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ ilf_type(X3,set_type)
| ~ member(X3,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_34,plain,
( subset(identity_relation_of(X1),cross_product(X1,X1))
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_35,negated_conjecture,
( ilf_type(esk12_0,set_type)
& ~ ilf_type(identity_relation_of(esk12_0),identity_relation_of_type(esk12_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])]) ).
cnf(c_0_36,plain,
( ilf_type(X1,identity_relation_of_type(X2))
| ~ ilf_type(X1,relation_type(X2,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_17]),c_0_17])]) ).
cnf(c_0_37,plain,
( ilf_type(X1,relation_type(X2,X3))
| ~ member(X1,power_set(cross_product(X2,X3))) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_38,plain,
( member(X1,power_set(X2))
| ~ member(esk6_2(X1,X2),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_39,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ subset(X3,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_17]),c_0_17]),c_0_17])]) ).
cnf(c_0_40,plain,
subset(identity_relation_of(X1),cross_product(X1,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_17])]) ).
cnf(c_0_41,negated_conjecture,
~ ilf_type(identity_relation_of(esk12_0),identity_relation_of_type(esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_42,plain,
( ilf_type(X1,identity_relation_of_type(X2))
| ~ member(X1,power_set(cross_product(X2,X2))) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_43,plain,
( member(esk6_2(X1,X2),X1)
| member(X1,power_set(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_44,plain,
( member(X1,power_set(X2))
| ~ member(esk6_2(X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_17]),c_0_17])]) ).
cnf(c_0_45,plain,
( member(X1,cross_product(X2,X2))
| ~ member(X1,identity_relation_of(X2)) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_46,negated_conjecture,
~ member(identity_relation_of(esk12_0),power_set(cross_product(esk12_0,esk12_0))),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,plain,
( member(esk6_2(X1,X2),X1)
| member(X1,power_set(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_17]),c_0_17])]) ).
cnf(c_0_48,plain,
( member(X1,power_set(cross_product(X2,X2)))
| ~ member(esk6_2(X1,cross_product(X2,X2)),identity_relation_of(X2)) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_49,negated_conjecture,
member(esk6_2(identity_relation_of(esk12_0),cross_product(esk12_0,esk12_0)),identity_relation_of(esk12_0)),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_50,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_46]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET666+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 13:12:57 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.56 start to proof: theBenchmark
% 0.21/0.58 % Version : CSE_E---1.5
% 0.21/0.58 % Problem : theBenchmark.p
% 0.21/0.58 % Proof found
% 0.21/0.58 % SZS status Theorem for theBenchmark.p
% 0.21/0.58 % SZS output start Proof
% See solution above
% 0.21/0.59 % Total time : 0.016000 s
% 0.21/0.59 % SZS output end Proof
% 0.21/0.59 % Total time : 0.019000 s
%------------------------------------------------------------------------------